Estimation of tension distribution on drumheads by visualization of high-order modes using Fourier transform profilometry

Abstract

In this study, higher vibration modes of drumheads were visualized using Fourier transform profilometry (FTP) for simplifying drum tuning process. In our previous work, we confirmed that images of the (1,1) mode of a drumhead had some curved nodal lines due to non-uniform tension and that it provided visual cues on the state of drum tuning. However, when there were two areas with low tension on a drumhead, non-uniform tension did not curve the nodal lines. Therefore, focusing only on the (1,1) mode can lead to misinterpreting a non-uniform state as uniform. In this research, we expand the scope of visualization to higher modes in order to alleviate this problem. If nodal lines can be visualized even in higher modes, information not included in the (1,1) mode can be obtained, which will allow us to know the tuning state more faithfully. In a visualization experiment, we focused mainly on the (2,1) mode, which consists of two nodal lines. FTP-based visualization confirmed that even when the tension distribution had two areas with low tension, those nodal lines curved around each area. Based on this, it became able to estimate tension distribution that had been challenging with only the (1,1) mode considered.